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The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

  • Jalil Manafian ORCID logo EMAIL logo , Onur Alp Ilhan and Laleh Avazpour
Published/Copyright: September 16, 2020
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 22 Issue 1

Abstract

In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β-derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β-derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Keywords: space-time (2 + 1)-dimensional breaking soliton equations; space-time fractional order Boussinesq equation; space-time fractional order SRLW equation; the β-derivative; the extended auxiliary equation mapping method
Corresponding author: Jalil Manafian, Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran, E-mail:

Acknowledgments

L.A. acknowledges support by DOE (award DE-SC0008712). The work was performed using the computer resources of the UW-Madison Center for High Throughput Computing (CHTC).

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work was not supported by any specific funding.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2019-11-10
Accepted: 2020-07-23
Published Online: 2020-09-16
Published in Print: 2021-02-23

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control
  4. Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays
  5. The monotone iterative method for the integral boundary value problems of fractional p-Laplacian equations with delay
  6. Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators
  7. Synchronization of Cohen-Grossberg fuzzy cellular neural networks with time-varying delays
  8. Application of Hermite–Padé approximation for detecting singularities of some boundary value problems
  9. The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs
  10. A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument
  11. Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models
  12. Synchronization stability on the BAM neural networks with mixed time delays
  13. Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method
https://doi.org/10.1515/ijnsns-2019-0279
Keywords for this article
space-time (2 + 1)-dimensional breaking soliton equations; space-time fractional order Boussinesq equation; space-time fractional order SRLW equation; the β-derivative; the extended auxiliary equation mapping method

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control
  4. Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays
  5. The monotone iterative method for the integral boundary value problems of fractional p-Laplacian equations with delay
  6. Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators
  7. Synchronization of Cohen-Grossberg fuzzy cellular neural networks with time-varying delays
  8. Application of Hermite–Padé approximation for detecting singularities of some boundary value problems
  9. The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs
  10. A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument
  11. Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models
  12. Synchronization stability on the BAM neural networks with mixed time delays
  13. Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method
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